Pith Number

pith:4UDKYXWF

pith:2015:4UDKYXWFFQ3GZ5UIJB7GXXO32W

not attested not anchored not stored refs pending

A solution to Open Problem 3.137 by O. Furdui on multiple factorial series

Ulrich Abel

arxiv:1508.04315 v1 · 2015-08-18 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UDKYXWFFQ3GZ5UIJB7GXXO32W}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:35:05.662800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e506ac5ec52c366cf688487e6bdddbd584d7a02b16524bc08d819d5d063b0d4f

Aliases

arxiv: 1508.04315 · arxiv_version: 1508.04315v1 · doi: 10.48550/arxiv.1508.04315 · pith_short_12: 4UDKYXWFFQ3G · pith_short_16: 4UDKYXWFFQ3GZ5UI · pith_short_8: 4UDKYXWF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4UDKYXWFFQ3GZ5UIJB7GXXO32W \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e506ac5ec52c366cf688487e6bdddbd584d7a02b16524bc08d819d5d063b0d4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "477bc9e7b08c8099efb45c4d036ffe01e14aed4abed7f77127a921b5bb93f81a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-18T13:42:44Z",
    "title_canon_sha256": "56fe79df7631e08876ff0c6b37c6312b87b91a2afce1222adef138e482f2af3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.04315",
    "kind": "arxiv",
    "version": 1
  }
}